First, take a deep breath. This should be recoverable, one way or another.

It sounds like you trimmed the corners off blocks, thinking you would then sew them onto different blocks. What measurements did you use, when cutting the corners off? Did you cut a full 2.5" in from the corner, or some other measurement? (I'm trying to figure out if the 2.5" squares are still useful to you).
If you cut at 2.5", then I think the only way to rescue this is going to be to trim your blocks. Sew the corners on as you have been doing, then carefully trim it square again. You should end up with a 7" block I think. The pattern will still work, but your quilt will be smaller (you can fix that by adding 1 row/column, if you have enough fabric to make more blocks). You will need to be very careful that you center the blocks when you trim, so that the corner triangles will all line up in the end.

Or, re-cut the 2.5" squares to a larger size, to match your trimmed block (this assumes you have more fabric). You would need to cut your squares 3 1/4", then cut them diagonally in half. The resulting triangle should fit the corner of your blocks correctly.

Another option that occurred to me, but I don't know how well it would work without having the blocks in front of me. Turn the blocks 45 degrees, and sew the corners to the straight (untrimmed) edges of the blocks. That edge might fit the 2.5" square better, and you wouldn't have to trim. But as I said, I can't tell for sure if that will work, and you will end up with bias edges to deal with. This may not be a great option for a new quilter.

One of the problems with the cut triangles is that they are now too small for the size of your larger squares. You can do one of 2 things. First off, I see that you cut the corners off your larger squares. So, I think the best and most cost effective way to fix this is this: Do you have more of the fabric that you are using for the corner squares? If you do, recut the squares. You can lay them RST on the bigger squares and then use the cut line as a guide and sew a scant 1/4" to attach the corner squares. Iron them open and trim them up to square your block.

The second way would involve cutting your larger squares down to fit the corner squares (which are now triangles). This is going to result in a much smaller snowball block.

Beautiful fabric!

Edited to add: Oops! Looks like a previous poster gave you the same information as I did!

No one has ever become poor by giving. - Anne Frank
Darkness cannot drive out darkness; only light can do that. Hate cannot drive out hate; only love can do that. - Martin Luther King, Jr.

Is there a local quilt shop near you? Or maybe a local church has a quilting group? It looks like you can save the blocks if you can get someone to show you how to lay a new corner block (of the right proportion)in place and sew, then trim only the corner block you have sewn to what is left of the larger part of the block. Your finished blocks may not be the finished size you were expecting and you may have to add another row to get the size quilt you want. Or add another border. I am pretty much a new quilter myself and I make plenty of mistakes. Sometimes I can't believe what I have done. But to make it work you just have to think about it and change it up a little. It may not look like the original plan but might be really cool. Good luck! And don't be afraid to ask around for a local quilter to help you. Someone from the board might even be close by. We come from everywhere to join in here.

"How do I make sure I'm super careful to center the blocks when I trim if I continue to do this the (incorrect) way that I started? Is there a tool I can buy to help me with this?"

If you cut new squares for your corners, I would cut them bigger than you need, sew, press and trim to size...AFTER you've sewn them on. That way, if they're not completely squared up with your edges, you can trim to square after they're sewn and pressed. I use one of the slotted cutting guides from June Taylor, the Shape Cut with half inch increments. I like it for cutting just about anything and squaring it up.

I read somewhere...it was an old pattern or article...to always make ONE BLOCK first before cutting all of your blocks...so you know how it will turn out...just in case you've read something wrong, or instructions are wrong. I hadn't thought of that, and I was always happily cutting all of my pieces...til I found a pattern that was off by a half inch for ONE of the pieces...

What to do now? Since you cut them, you are working with a bias. The bias will stretch. I would spray starch them several times until they are kinda stiff, then sew them. That will help hold the bias when you sew them. It isn't a perfect solution, but it will help.

The question is: how big a piece do I need to cut to have a 1/4" seam allowance and fill in the space in the corner from cutting off those 3" x 3" x 4.25" triangles? Trust me, if those spaces are not 3" x 3" x 4.25" geometry professors will beat down your door because you just disproved Pythagoras' famous theorem.

Here is what you can do to do the least work. If you have any fabric left that matches your snowball bodies, cut it into 4" squares (the actual theoretical size is 3 7/8"' but I don't cut that accurately). Starch it before cutting. Cut each square along the diagonal, giving you two equal sized triangles.

Carefully, because you have bias edges, match the long edge of this triangle with the long side of the space in the corners. Part of the triangle will be longer; that is the way it should be. They look little ears. The raw edges should meet 1/4" in from the cut edge, where your seam line will be. Sew the two pieces together using a 1/4 seam. Press the triangle piece into the corner. Press, don't iron. Trim off the little ears. You may need to trim off a little bit on the outside edges of the triangle, but it will only be about 1/16".

If you need to buy more fabric, you can cut about 10 squares or 20 triangles from each 4" of 40" wide fabric.

I arise in the morning torn between a desire to improve the world and a desire to enjoy the world. This makes it hard to plan the day.

How do I make sure I'm super careful to center the blocks when I trim if I continue to do this the (incorrect) way that I started? Is there a tool I can buy to help me with this?

I don't know about a tool that would do this. I think you just need to figure out the measurement and use a square to trim them all. The important thing is going to be to make sure you have exactly the same size corners on all the blocks after you trim. So taken one block, lay a square ruler on top of it and see what size block you think you can cut. Without having it in front of my, it's hard to say, but if you are adding 3x3x4 triangles to the blocks I think you'll get around 2 1/4" corners in the end, with about 3.5" along the edge of your snowball block. But don't take those measurements as true - you need to try it with a block. Just make sure when you trim that you have the same size triangle on each edge. Once you find the right measurements, you might want to mark your ruler with tape, so you can align all the blocks the same way.

If you have enough fabric to recut the corner squares, the measurement you need is 4 1/4" to fit the 3x3x4" triangles you cut off the snowballs. A hint - try this on one block, before you cut a lot of squares. This is a good idea for any quilt you are making - sometimes the pattern is wrong and it's better to find out before you cut too much.

If you've already trimmed all of them, you can save them by cutting new squares for the corners. I'm thinking 2 3/4, but I'd do a sample with paper before I cut any more fabric. Your 2 1/2 squares can be saved for for another project - that's a common size. 2 1/2 was small for a 8 1/2 block anyhow. Okay, I just did a 2 3/4" one and you should be okay. You cut on the 2 1/2 line and you need the extra 1/4 for the seam. Do not trim off the underside until the block has all four corners done, and is pressed and squared. I find I have to sew a hair inside the line in order to have the corner be exact. You've got to allow for the seam and the little lost in pressing it back on itself.

Draw the diagonal on the square, carefully line it the square up with where the missing corner would be, put in 2 pins and sew it from the square side so you can see the line. Do not try to use that bias edge to line up your 1/4" seam.
It will be fine and your snowballs will be a little rounder, but I like that. The ones I'm working on are 2 1/2" on a 4 1/2" block. I used 3 1/3 on 7 1/2 inch blocks, so 2 1/2 is not written in stone.

Relax, take a deep breath, have a chocolate and cut new corners. Come back if you need anything else. You can't believe the questions I asked a year and half ago.